CN109470653B - Method for analyzing optical characteristics of film-substrate-film system containing substrate characteristics - Google Patents

Method for analyzing optical characteristics of film-substrate-film system containing substrate characteristics Download PDF

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CN109470653B
CN109470653B CN201811308241.7A CN201811308241A CN109470653B CN 109470653 B CN109470653 B CN 109470653B CN 201811308241 A CN201811308241 A CN 201811308241A CN 109470653 B CN109470653 B CN 109470653B
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refractive index
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刘华松
王利栓
李士达
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Tianjin Jinhang Institute of Technical Physics
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    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
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    • G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
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Abstract

The invention belongs to the technical field of optical films, and particularly relates to a method for analyzing optical characteristics of a film-substrate-film system containing substrate characteristics. The substrate of the optical film presents a subsurface damage layer during processing, which inevitably affects the performance of the high performance optical film. The method is to equivalently use a sub-surface layer as a graded-index film, add two layers of graded-index films on two sides of a substrate, wherein the initial optical constant of the graded-index film is the same as that of a bulk material, and the two layers of graded-index layers and multilayer films on two surfaces respectively form a complete film-substrate-film system. The method has universality for the calculation and evaluation of the optical characteristics of all film-substrate-film systems.

Description

Method for analyzing optical characteristics of film-substrate-film system containing substrate characteristics
Technical Field
The invention belongs to the technical field of optical films, and particularly relates to a method for analyzing optical characteristics of a film-substrate-film system containing substrate characteristics.
Background
Ultra-precise optical elements are used in a variety of advanced technical fields, such as short-wavelength optical and high-light optical systems, such as X-ray optical systems, ultraviolet optical systems, chemical laser systems, high-power laser systems, laser resonator mirrors, laser gyro reflectors, and the like. The ultra-precise optical element not only requires a high-quality optical substrate, but also has a precise single-layer or multi-layer complex film structure matched with the substrate to realize its unique function.
Americans have tried to design multilayer antireflection films since 1938 until 1949 to arrive at a satisfactory solution for a dual layer antireflection film system; in 1965, a three-layer antireflection film system structure appears, so that broadband antireflection can be realized, and the film system is simpler and easier to calculate due to the auxiliary design of an electronic computer. However, in recent years, in view of the development of high-end optoelectronic devices and advanced optical systems, more stringent requirements are put on the optical performance of the optical thin film, and the optical performance of the ultra-precise optical thin film element is related to the state of the substrate surface on which the element is deposited.
The cold working process of the optical substrate generally includes the steps of rough grinding, finish grinding, rough polishing, and finish polishing. The last polishing process is the most critical process of the ultra-precision machining technology, and the process can remove a surface damage layer generated after the machining of the previous process, reduce surface defects and finish the surface shape, and is an effective way for realizing the high precision of the optical parts. In recent years, with the continuous deep understanding of the mechanism of forming the surface of the nanometer-scale ultra-precise element and the improvement of the technical level of detecting the nanometer-scale surface, the chemical, magnetic flow, acoustic and energy field technologies are applied to the improvement of the polishing technology in succession, so that a plurality of novel polishing methods are generated. To date, it has become possible to obtain high precision surfaces at the atomic level by polishing. Nevertheless, the subsurface damage layer of the optical substrate, which is different from the bulk material of the substrate in structure and composition and therefore also has a difference in refractive index, is not completely eliminated, and tends to affect the spectral performance of the entire film-substrate-film system.
In summary, when the sub-surface damage of the optical film substrate exists, how to design and analyze the optical performance of the film-substrate-film system containing the sub-surface damage characteristic becomes one of the important problems in the design, analysis and manufacture of the high-performance optical film element at present.
Disclosure of Invention
Technical problem to be solved
The technical problem to be solved by the invention is as follows: how to solve the problem of calculating and analyzing the optical performance of a film-substrate-film system with a substrate having subsurface damage characteristics.
(II) technical scheme
In order to solve the above technical problems, the present invention provides a method for analyzing optical characteristics of a thin film-substrate-thin film system having a substrate feature, comprising the steps of:
step 1: firstly, the surface of a substrate is assumed to be smooth, and the surface roughness is far less than the working wavelength;
step 2: determining the characteristics of the subsurface according to the characteristics of the actual processing of the optical substrate, and enabling the subsurface to be equivalent to a graded-index film with negative refractive index gradient, wherein the refractive index gradient is delta; the thickness of the subsurface damage layer is dsubThe refractive index of the bulk substrate material is NsAnd T is a fitting coefficient, the refractive index equation of any point from the substrate to the surface is as follows:
Figure GDA0002812573000000021
wherein, the distance between the point and the substrate is marked as x;
and step 3: carrying out plane slicing on the subsurface layer, wherein the number of the tangent plane layers is N, and the thickness of each layer of slice is dsubN, thickness of planar slice not more than 1 times lambda0，λ0Is the operating wavelength or the center wavelength of the operating spectrum; the complex refractive index of the slice of the j-th layer is:
Figure GDA0002812573000000022
wherein i is the imaginary sign of the complex number;
and 4, step 4: at an incident angle theta0In the case of (2), the refractive index of the incident medium is N0Then, the equivalent refractive index of the two surfaces of the incident medium and the material is calculated as follows:
the equivalent refractive index of the incident medium is:
Figure GDA0002812573000000031
the equivalent refractive index of the jth planar slice in the subsurface is:
Figure GDA0002812573000000032
the equivalent refractive index of the kth film in the multilayer film is as follows:
Figure GDA0002812573000000033
determination of angle of refraction θ in layer j planar slice using Fresnel's lawjAngle of refraction in the k-th filmkAnd angle of refraction in the substrate thetas：
N0,s,psinθ0＝Nj,s,psinθj＝Nk,s,psinθk＝Ns,s,psinθs (6)
And 5: considering the above-mentioned substrate subsurface presence, the ideal thin film-substrate-thin film system is modified to a thin film-subsurface-substrate-subsurface-thin film system, the transmission matrix γ of the multilayer film is modified to:
Figure GDA0002812573000000034
wherein, deltajAnd deltakPhase thickness of the sub-surface j slice and phase thickness, η, of the film ksFor the admittance of the substrate, M is the number of layers of the multilayer film.
Step 6: the internal transmittance u of the substrate is calculated. Angle of refraction in the substrate of thetasAngle of refraction thetajThe sine and cosine of (c) are expressed as follows:
sinθs＝s'+js" cosθj＝c'+jc" (8)
wherein s ', s ", c', c" are sine and cosine coefficients, respectively;
equivalent refractive index N of substrateqThe following can be written:
Figure GDA0002812573000000041
light propagation angle in the substrate
Figure GDA0002812573000000042
The Fresnel refraction law is satisfied:
Figure GDA0002812573000000043
equivalent extinction coefficient K and equivalent refractive index N of substrateqThe following relation is satisfied:
Figure GDA0002812573000000044
the internal transmission u of the substrate is thus expressed as follows:
Figure GDA0002812573000000045
wherein d issIs the thickness of the substrate;
and 7: based on the principle of linear superposition of optical intensity, the method for calculating the optical characteristics of the film-substrate-film system containing the subsurface features comprises the following steps:
the reflectivity R is:
Figure GDA0002812573000000046
the transmittance T is:
Figure GDA0002812573000000047
wherein R isafForward reflectance, R, of a subsurface-thin film system that is a front surfaceafaIs the retroreflectivity, TfaIs the transmittance of the film layer, RbfaRetroreflectivity, T, of a sub-surface-thin film system being the back surfacefbThe transmittance of the film layer can be calculated by the optical film principle of the multilayer film.
(III) advantageous effects
Compared with the prior art, the invention provides a method for calculating and analyzing the optical performance of a film-substrate-film system containing the processing characteristics of the surface of the substrate. The method is characterized in that a subsurface is equivalent to a graded-index film, the film is subjected to plane slicing treatment, an electric field transmission matrix of a multilayer film is corrected, then optical characteristics of two surfaces of a substrate are obtained, and finally the optical characteristics of the whole system are obtained based on a light wave linear superposition principle. The method has universality for calculation and analysis of the optical performance of the multilayer film of the optical substrate made of any material, and especially has important guiding significance for high-performance transmission optical thin film elements.
Drawings
FIG. 1 is a graph showing optical constants of a zinc sulfide material.
FIG. 2 is a graph showing the refractive index gradient as a function of subsurface zinc sulfide.
Fig. 3 is a characteristic diagram of the surface antireflection film.
Fig. 4 is a reflectance spectrum of the modified film-zinc sulfide-film system.
Fig. 5 is a graph of the transmittance spectrum of the modified film-zinc sulfide-film system.
FIG. 6 is a graph showing optical constants of fused silica.
FIG. 7 is a graph showing the refractive index gradient as a function of the subsurface of fused silica.
FIG. 8 is a characteristic diagram of a short pass film on the front surface of fused silica.
Fig. 9 is a characteristic diagram of an antireflection film on the rear surface of fused silica.
FIG. 10 is a reflectance spectrum of a modified thin film-fused silica-thin film system.
FIG. 11 is a graph of the transmittance spectrum of the modified film-fused silica-film system.
Fig. 12 is a schematic diagram of the technical solution of the present invention.
Detailed Description
In order to make the objects, contents, and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
In order to solve the problems of the prior art, the present invention provides a method for analyzing optical characteristics of a thin film-substrate-thin film system having substrate features, as shown in fig. 12, comprising the following steps:
step 1: firstly, the surface of a substrate is assumed to be smooth, and the surface roughness is far less than the working wavelength;
step 2: determining the characteristics of the subsurface according to the characteristics of the actual processing of the optical substrate, and enabling the subsurface to be equivalent to a graded-index film with negative refractive index gradient, wherein the refractive index gradient is delta; the thickness of the subsurface damage layer is dsubLarge block baseThe refractive index of the base material is NsAnd T is a fitting coefficient, the refractive index equation of any point from the substrate to the surface is as follows:
Figure GDA0002812573000000061
wherein, the distance between the point and the substrate is marked as x;
and step 3: carrying out plane slicing on the subsurface layer, wherein the number of the tangent plane layers is N, and the thickness of each layer of slice is dsubN, thickness of planar slice not more than 1 times lambda0，λ0Is the operating wavelength or the center wavelength of the operating spectrum; the complex refractive index of the slice of the j-th layer is:
Figure GDA0002812573000000062
and 4, step 4: at an incident angle theta0In the case of (2), the refractive index of the incident medium is N0Then, the equivalent refractive index of the two surfaces of the incident medium and the material is calculated as follows:
the equivalent refractive index of the incident medium is:
Figure GDA0002812573000000063
the equivalent refractive index of the jth planar slice in the subsurface is:
Figure GDA0002812573000000064
the equivalent refractive index of the kth film in the multilayer film is as follows:
Figure GDA0002812573000000065
determination of angle of refraction θ in layer j planar slice using Fresnel's lawjAngle of refraction in the k-th filmkAnd angle of refraction in the substrate thetas：
N0,s,psinθ0＝Nj,s,psinθj＝Nk,s,psinθk＝Ns,s,psinθs (6)
And 5: considering the above-mentioned substrate subsurface presence, the ideal thin film-substrate-thin film system is modified to a thin film-subsurface-substrate-subsurface-thin film system, the transmission matrix γ of the multilayer film is modified to:
Figure GDA0002812573000000071
wherein, deltajAnd deltakPhase thickness of the sub-surface j slice and phase thickness, η, of the film ksFor the admittance of the substrate, M is the number of layers of the multilayer film.
Step 6: the internal transmittance u of the substrate is calculated. Angle of refraction in the substrate of thetasAngle of refraction thetajThe sine and cosine of (c) are expressed as follows:
sinθs＝s'+js" cosθj＝c'+jc" (8)
wherein s ', s ", c', c" are sine and cosine coefficients, respectively;
equivalent refractive index N of substrateqThe following can be written:
Figure GDA0002812573000000072
light propagation angle in the substrate
Figure GDA0002812573000000073
The Fresnel refraction law is satisfied:
Figure GDA0002812573000000074
equivalent extinction coefficient K and equivalent refractive index N of substrateqThe following relation is satisfied:
Figure GDA0002812573000000075
the internal transmission u of the substrate is thus expressed as follows:
Figure GDA0002812573000000076
wherein d issIs the thickness of the substrate;
and 7: based on the principle of linear superposition of optical intensity, the method for calculating the optical characteristics of the film-substrate-film system containing the subsurface features comprises the following steps:
the reflectivity R is:
Figure GDA0002812573000000077
the transmittance T is:
Figure GDA0002812573000000078
wherein R isafForward reflectance, R, of a subsurface-thin film system that is a front surfaceafaIs the retroreflectivity, TfaIs the transmittance of the film layer, RbfaRetroreflectivity, T, of a sub-surface-thin film system being the back surfacefbThe transmittance of the film layer can be calculated by the optical film principle of the multilayer film.
Example 1
In this embodiment:
example (c): the spectral characteristic of the antireflection film on the surface of the 6mm zinc sulfide material is 7.5-9.7 mu m;
1) the optical constants of the zinc sulfide material are shown in figure 1;
2) the sub-surface layer of the zinc sulfide material is layered into 1000 layers, the thickness is 10 μm, the refractive index gradient is-2%, and the refractive index function of the equivalent graded-index film is shown in figure 2;
3) the forward reflectance, backward reflectance and transmittance spectra of both surfaces of zinc sulfide are shown in FIG. 3;
4) the reflectivity spectrum of the film-zinc sulfide-film system is shown in figure 4, and compared with the situation without subsurface damage, the shape of the reflectivity spectrum is similar, but the central wavelength is shifted, and the reflectivity spectrum of different wavelengths is modulated;
5) the transmittance spectrum of the film-zinc sulfide-film system is shown in fig. 5, and compared to the case without subsurface damage, the reflectance spectrum is similar in shape, but the center wavelength is shifted and the reflectance spectrum is modulated at different wavelengths.
Example 2
In this embodiment:
example (c): the 532nm wavelength frequency doubling separation film on the surface of the fused quartz has the spectral characteristic;
1) the optical constants of the fused silica material are shown in FIG. 6;
2) the subsurface layer of the fused silica material is layered into 1000 layers, the thickness is 10 μm, the refractive index gradient is-5%, and the refractive index function of the equivalent graded-index film is shown in figure 7;
3) the forward reflectance, backward reflectance and transmittance spectra of the first surface short-wavelength pass multilayer film are shown in FIG. 8;
4) the reflectance and transmittance spectra of the second surface anti-reflective multilayer film are shown in fig. 9;
5) the reflectivity spectrum of the short wave pass film-fused silica-antireflection film system is shown in figure 10, the transmittance of 532nm is mainly concerned, and compared with the case without subsurface damage, the reflectivity is increased from 0.05% to 0.29%;
6) the transmittance spectrum of the short-wave pass film-fused silica-antireflection film system is shown in figure 11, and compared with the case without subsurface damage, the transmittance at 532nm wavelength is reduced from 99.91% to 99.67%.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (1)

1. A method for analyzing optical characteristics of a film-substrate-film system having substrate features, comprising the steps of:
step 1: firstly, the surface of a substrate is assumed to be smooth, and the surface roughness is far less than the working wavelength;
step 2: determining the characteristics of the subsurface according to the characteristics of the actual processing of the optical substrate, and enabling the subsurface to be equivalent to a graded-index film with negative refractive index gradient, wherein the refractive index gradient is delta; the thickness of the subsurface damage layer is dsubThe refractive index of the bulk substrate material is NsAnd T is a fitting coefficient, the refractive index equation of any point from the substrate to the surface is as follows:
Figure FDA0002812572990000011
wherein, the distance between the point and the substrate is marked as x;
and step 3: carrying out plane slicing on the subsurface layer, wherein the number of the tangent plane layers is N, and the thickness of each layer of slice is dsubN, thickness of planar slice not more than 1 times lambda0，λ0Is the operating wavelength or the center wavelength of the operating spectrum; the complex refractive index of the slice of the j-th layer is:
Figure FDA0002812572990000012
wherein i is the imaginary sign of the complex number;
and 4, step 4: at an incident angle theta0In the case of (2), the refractive index of the incident medium is N0Then, the equivalent refractive index of the two surfaces of the incident medium and the material is calculated as follows:
the equivalent refractive index of the incident medium is:
Figure FDA0002812572990000013
the equivalent refractive index of the jth planar slice in the subsurface is:
Figure FDA0002812572990000014
the equivalent refractive index of the kth film in the multilayer film is as follows:
Figure FDA0002812572990000021
determination of angle of refraction θ in layer j planar slice using Fresnel's lawjAngle of refraction in the k-th filmkAnd angle of refraction in the substrate thetas：
N0,s,psinθ0＝Nj,s,psinθj＝Nk,s,psinθk＝Ns,s,psinθs (6)
And 5: considering the above-mentioned substrate subsurface presence, the ideal thin film-substrate-thin film system is modified to a thin film-subsurface-substrate-subsurface-thin film system, the transmission matrix γ of the multilayer film is modified to:
Figure FDA0002812572990000022
wherein, deltajAnd deltakPhase thickness of the sub-surface j slice and phase thickness, η, of the film ksIs the admittance of the substrate, and M is the number of layers of the multilayer film;
step 6: calculating the internal transmittance u of the substrate; angle of refraction in the substrate of thetasAngle of refraction thetajThe sine and cosine of (c) are expressed as follows:
sinθs＝s'+js" cosθj＝c'+jc" (8)
wherein s ', s ", c', c" are sine and cosine coefficients, respectively;
equivalent refractive index N of substrateqThe following can be written:
Figure FDA0002812572990000023
light propagation angle in the substrate
Figure FDA0002812572990000024
The Fresnel refraction law is satisfied:
Figure FDA0002812572990000025
equivalent extinction coefficient K and equivalent refractive index N of substrateqThe following relation is satisfied:
Figure FDA0002812572990000026
the internal transmission u of the substrate is thus expressed as follows:
Figure FDA0002812572990000027
wherein d issIs the thickness of the substrate;
and 7: based on the principle of linear superposition of optical intensity, the method for calculating the optical characteristics of the film-substrate-film system containing the subsurface features comprises the following steps:
the reflectivity R is:
Figure FDA0002812572990000031
the transmittance T is:
Figure FDA0002812572990000032
wherein R isafForward reflectance, R, of a subsurface-thin film system that is a front surfaceafaIs the retroreflectivity, TfaIs the transmittance of the film layer, RbfaRetroreflectivity, T, of a sub-surface-thin film system being the back surfacefbThe transmittance of the film layer can be calculated by the optical film principle of the multilayer film.
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